A note on BV and 1-Sobolev functions on the weighted Euclidean space

DOI10.4171/rlm/988zbMath1529.46024arXiv2110.02622OpenAlexW3201713159MaRDI QIDQ6111613

Maria Stella Gelli, Danka Lučić

Publication date: 4 August 2023

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.02622

zbMATH Keywords

functions of bounded variationsweighted Euclidean spacetangent space with respect to a measure

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (2)

Mass Optimization Problem with Convex Cost ⋮ Dirichlet or Neumann problem for weighted 1-Laplace equation with application to image denoising

Cites Work

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• Decomposition of acyclic normal currents in a metric space
• Some results on Sobolev spaces with respect to a measure and applications to a new transport problem
• Functions of bounded variation on ``good metric spaces
• Second-order energies on thin structures: Variational theory and non-local effects
• Structure of metric cycles and normal one-dimensional currents
• Characterisation of upper gradients on the weighted Euclidean space and applications
• Infinitesimal hilbertianity of locally \(\mathrm{CAT}(\kappa)\)-spaces
• Setting the free material design problem through the methods of optimal mass distribution
• Optimal design versus maximal Monge-Kantorovich metrics
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• Lectures on nonsmooth differential geometry
• \(\Gamma\)-convergence of nonconvex integrals in Cheeger-Sobolev spaces and homogenization
• Energies with respect to a measure and applications to low dimensional structures
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Homogenization of elasticity problems on singular structures
• Sobolev Spaces on Metric Measure Spaces
• Characterization of optimal shapes and masses through Monge-Kantorovich equation

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